Internal problem ID [5823]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 2. Linear homogeneous equations. Section 2.3.4 problems. page 104
Problem number: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime } x +x y^{\prime }-y=x^{2}+2 x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve(x*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=x^2+2*x,y(x), singsol=all)
\[ y \left (x \right ) = -c_{2} {\mathrm e}^{-x}+x \left (c_{2} \operatorname {expIntegral}_{1}\left (x \right )+x +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.274 (sec). Leaf size: 31
DSolve[x*y''[x]+x*y'[x]-y[x]==x^2+2*x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -c_2 x \operatorname {ExpIntegralEi}(-x)+x^2+c_1 x-c_2 e^{-x} \]